Clean Price, Dirty Price, and the Interest You Owe the Seller
Bonds are quoted at one price and settle at a higher one. The difference is interest that accrued to the previous holder, and forgetting it is a classic beginner error.
The Two Prices
Bonds pay coupons periodically, typically twice a year. Between payment dates, interest is accumulating for whoever holds the bond, even though no cash has arrived.
If you sell a bond four months into a six month coupon period, you have earned four months of interest and are about to receive nothing, because the next full payment goes to the new holder. The market solves this by making the buyer pay you for it.
The clean price is what is quoted. The dirty price, sometimes called the full or invoice price, is the clean price plus accrued interest, and it is what actually changes hands.
The Calculation
Accrued interest is the coupon multiplied by the fraction of the period that has elapsed.
A bond with a 1,000 par value and a 5 percent coupon pays 25 dollars every six months. If 120 of the 181 days in the period have passed, accrued interest is 25 times 120 divided by 181, or 16.57 dollars.
Buy that bond at a quoted clean price of 980 and you send 996.57. In four months you will receive the full 25 dollar coupon, of which 16.57 was really a refund of what you advanced.
The buyer is not paying extra. They are prepaying the portion of the next coupon that belongs to someone else, and getting it back in a lump when the coupon lands.
Why Quote Clean at All
Because the dirty price contains a sawtooth. It climbs steadily as interest accrues, then drops by the coupon amount on payment day, then climbs again. That pattern has nothing to do with the value of the bond and would obscure every real price movement.
The clean price strips the sawtooth out and moves only when yields, credit, or supply and demand move. Comparing two bonds on clean price is comparing them on something meaningful. Comparing dirty prices means comparing where each happens to sit in its coupon cycle.
Day Count Conventions
The fraction of the period elapsed sounds simple and is not, because different markets count days differently.
| Convention | Method | Typical use |
|---|---|---|
| Actual over actual | Real days over real days | US Treasuries |
| 30 over 360 | Every month is 30 days | US corporates and municipals |
| Actual over 360 | Real days, 360 day year | Money markets |
These produce slightly different accrued amounts on the same bond and the same dates. On a large trade the difference is real money, which is why the convention is part of the security's terms rather than an operational footnote.
Where It Matters
Three practical consequences. Settlement amounts never match the quoted price, so anyone reconciling a trade against a screen quote will find a discrepancy that is not an error.
Yield calculations use the dirty price, since that is the actual cash outlay. Using the clean price overstates yield slightly.
And bonds in default trade flat, meaning without accrued interest, because interest that will not be paid should not be charged to a buyer. A quote convention change is one of the signals that the market has stopped believing the issuer will perform.
The Bottom Line
The clean price is the quote and the dirty price is the cheque. The gap is accrued interest, owed to the seller for the portion of the coupon period they held the bond, and it is returned to the buyer at the next payment. It is bookkeeping rather than economics, and it is the reason the amount leaving your account never matches the price you agreed.